The British-English noun fly-tipping denotes the unauthorised dumping of building rubble, household refuse or other waste, especially while in the process of transporting it.

Here:
– fly refers to the phrase on the fly, meaning while in motion or progress;
– tipping is the gerund of the verb tip, in the sense to dump—from the sense to cause [the contents of a container] to be emptied out by tilting it.

These are the earliest occurrences of the noun fly-tipping that I have found, in chronological order:

1-: From the West London Press (London, England) of Friday 27^th June 1947—N.F.S. is the abbreviation of National Fire Service:

Fire Brigade Join Council In Rubbish Clearance

In Chelsea, the N.F.S. are actively co-operating with the Public Health Department in an endeavour to reduce complaints arising from the indiscriminate depositing of rubbish in static water tanks.
Chelsea, some time ago, referred this nuisance to the Metropolitan Boroughs Standing Joint Committee, with the suggestion that representation be made to the Ministry of Health “with a view to hastening the new procedure for the clearance of refuse and debris from bombed sites, and for the protection of such sites against fly tipping.” But the joint committee decline to take action.
State the Works and Highways Committee: “We deplore the delay in the clearance of these sites, but, unfortunately, we have no statutory authority on public health grounds, to take any action in the matter, beyond insisting on the removal of obnoxious refuse which has become a nuisance to public health.”

2-: From the West London Observer (London, England) of Friday 25^th November 1949:

METROPOLITAN BOROUGH OF HAMMERSMITH
CONFIRMATION OF BYELAW

NOTICE IS HEREBY GIVEN that the Council of the Metropolitan Borough of Hammersmith intend after the expiry of the period mentioned below to apply to the Secretary of State for confirmation of a byelaw made by the Council with respect to fly tipping on vacant sites.
Copies of the Byelaw will be kept at the office of the Council at the Town Hall, King Street, Hammersmith, W.6, and will be open to inspection without payment on any week-day during the usual office hours for one calendar month from and after the date of the publication of this notice. Copies of the Byelaw will also be supplied on receipt of an application accompanied by a fee of 6d. for each copy.
Any objection to the confirmation of the Byelaw may be made by letter addressed to the Under Secretary of State, Home Office, Whitehall, London, S.W.1, before the Byelaw is confirmed.
HORACE SLIM, Town Clerk.
Town Hall,
Hammersmith, W. 6.
17^th November, 1949.

A back-formation from the noun fly-tipping, the verb fly-tip means to illegally dump waste.

These are the earliest occurrences of the verb fly-tip that I have found, in chronological order:

1-: From the Sunday Mirror (London, England) of Sunday 15^th October 1967—the past participle fly-tipped is used adjectivally:

The problem of “fly-tipping” is alarming the council in the Royal Borough of Kensington and Chelsea, in London.
In an article in the council’s bulletin, Councillor Frank Thackway reports that the situation is serious.
He writes: “There has for many years been persistent dumping of unwanted household goods in the street—but ‘fly-tipping’ constitutes an appalling danger to blind, elderly or infirm people, and traffic.”
He says the trouble is mainly caused by lorry drivers who, instead of dumping rubble in authorised places, “simply dump the lot in the street.”
He adds: “Imagine the predicament of a blind person walking into an unexpected pile of rubble, full of broken glass and upturned nails. Serious injury could easily result.
“The extent of this problem is tremendous. More than 1,000 tons of fly-tipped material have been removed from public highways in one year—more than 600 tons were removed from a single street in six months—and at one time the incredible figure of 60 tons in a week was being removed.”

2-: From The Birmingham Post (Birmingham, Warwickshire, England) of Friday 15^th August 1969:

Six fined for tipping
Birmingham Public Works Committee is continuing its battle against people who “fly-tip” rubbish.
Recently the city has prosecuted six offenders, who were fined a total of £43 and were also ordered to pay costs.

The noun fly-tipper designates a person who illegally dumps waste.

These are the earliest occurrences of the noun fly-tipper that I have found, in chronological order:

1-: From The Shepherds Bush Gazette Hammersmith Post (London, England) of Thursday 3^rd September 1964:

SHANTY TOWN W.6
Almshouse site puts families in fear

A web of terror it spreading its tentacles out from the almshouse plot in Hammersmith’s Goldhawk-road.
Nearby residents walk warily past. Nightly a ginger headed teenage tough leads his gang to ‘play.’ Behind the surrounding advertisement hoarding buildings are pulled down. Bricks are thrown without a thought.
This is the site Hammersmith Charities Trust have earmarked for almshouses. […]
[…]
Adding to the general chaos are the fly-tippers. The site walls have been battered down by Ginger and his mates. Nightly lorries rev up to the gaps. In the morning there is another pile of old mattresses and fireplaces.

2-: From the Kensington Post (London, England) Friday 9^th July 1965:

Search for Maida Vale fly-tippers

Police are trying to trace the drivers of two lorries who dumped a pile of stone and rubble outside St. George’s School, Lanark Road, Maida Vale, last Wednesday.
Following complaints from the headmaster of the school, Mr. G. Curran, Westminster City Council workmen were sent to remove the rubble.
A police spokesman at Harrow Road explained that fly-tippers often dumped rubble in this way “so as to make a larger profit.”